We have performed extensive experimental and numerical studies of spontaneous percolation of small beads through an unconsolidated porous media made with large glass beads. In this paper, an experimental setup and a fast "discrete element method" algorithm are presented to deal with large numbers of particles during our interparticle percolation phenomenon studies. In all the experimental and numerical analyses, the size ratio between the moving beads and the stable packing was chosen larger than the geometrical trapping threshold: ξc=((2/(√3−1))^−1=6.464.... We measure the longitudinal and transverse dispersion coefficients versus the height of the porous medium or the number of falling small beads. The influence of bead properties such as density, diameter, or restitution coefficients was investigated by using either steel or glass beads. The individual description of these effects and their explanations were made possible by confrontation and coupling between experimental and numerical results. Indeed, with our numerical model, individual analysis of the effects of these mechanical or geometrical parameters were made possible and carried out.